Tentukan nilai lim (x-->0) (sin x - tan x)/(x^(2) tan x)!

<p>Jawaban: -1/2</p><p>&nbsp;</p><p>Konsep:</p><p>&gt;&gt; lim (x→0) (sin ax)/(bx) = a/b</p><p>&gt;&gt; lim(x→c) k · f(x) = k · lim(x→c) f(x)</p><p>&gt;&gt; cos 2x = 1 - 2 sin² x</p><p>&nbsp;</p><p>Pembahasan:</p><p>lim (x→0) (sin x - tan x)/(x² tan x)</p><p>= lim (x→0) (sin x - sin x/cos x)/(x² tan x)</p><p>= lim (x→0) ((sin x cos x - sin x)/cos x)/(x² · sin x/cos x)</p><p>= lim (x→0) (sin x(cos x - 1)/cos x) · (cos x)/(x² · sin x)</p><p>= lim (x→0) (cos x - 1)/x²</p><p>= lim (x→0) ((1 - 2 sin² (1/2)x) - 1)/x²</p><p>= lim (x→0) (-2 sin² (1/2)x)/x²</p><p>= lim (x→0) (-2 sin (1/2)x · sin (1/2)x)/(x · x)</p><p>= lim (x→0) -2 sin ((1/2)x)/(x) · sin ((1/2)x)/(x)</p><p>= -2 · lim (x→0) sin ((1/2)x)/(x) · sin ((1/2)x)/(x)</p><p>= -2 · (1/2)/1 · (1/2)/1</p><p>= -1/2</p><p>&nbsp;</p><p>Jadi, &nbsp;hasilnya adalah -1/2.</p>